At last count (last I heard anyway), Jupiter has 62 moons, while Saturn has 35. Mars has 2 moons.

However, the majority of the moons of Jupiter and Saturn, and all of Mar's moons are little more than captured asteroids. They're not even spherical.

Tradition aside, should these satellites be counted as moons?
Or should the term "moon" be restricted to bodies large enough to become spherical under their own gravity, aka big and round.

And if not, what exactly would the lower cut off limit be for determining if something is a moon, or just a satellite body? Surely a rock the size of a baseball cannot be called a moon...

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But he that sows lies in the end shall not lack of a harvest, and soon he may rest from toil indeed while others reap and sow in his stead. -J.R.R. Tolkien, The Silmarillion